No-arbitrage pricing in continuous-time models. Completeness. Fundamental Theorem of Asset Pricing. Applications of martingales. Multidimensional Brownian motion in asset price models. Other asset price models. Pricing of path-dependent options. Computation methods.
Intended learning outcomes
Students completing this subject should
know how to derive the Black-Scholes formula;
be familiar with the behaviour and computation of option prices;
be able to apply multidimensional Brownian motion in finance and insurance;
know some of the alternatives to Brownian motion in securities modelling;
be able to apply those techniques to actuarial problems.
Generic skills
High level of development: written communication; problem solving; statistical reasoning; application of theory to practice; interpretation and analysis; critical thinking.
Some level of development: synthesis of data and other information; evaluation of data and other information.